It is meat, but nobody died for it to become food. Also it never had a face. It is probably okay as far as the vegan issue is concerned.
As a matter of fact the proteins she will probably get from the placenta would be very good for her considering she has just finished growing a baby and she is probably going to be breastfeeding that baby. Those things take a lot of energy and a lot of vitamins.
If she wants to, then she should. If she changes her mind at the last minute, don't make an issue of it, just have another all natural back-up plan ready.
For instance: Many cultures have the mother bury the placenta in a special place known only to her. If she changes her mind about eating it, she might be open to that suggestion. Personally I would not advise suggesting that unless she starts to wonder about the first plan. New mommies have a funny way of having unscheduled emotional outbursts over any number of "very important" issues.
Of course if she has the baby in the hospital they probably won't let her eat the placenta. They are really funny about things like that. They didn't even like the idea of having the baby in a squatting position at the hospital I went to.
Added comment: Also I am pretty sure that she can drink her own breast milk and still be a vegan. Breast milk will not make her sick. It is delicious and very healthy. She should save most of it for the baby, though. Leave the colostrum for the baby. That has the antibodies that the baby needs to stay healthy.
Oh! When her milk comes in, about 2 or 3 days after the baby is born, she will need some help dealing with the swollen and sore breasts. You can drink some of the milk for her. Also bags of frozen peas or corn are very helpful for relieving some of the swelling and pain.
I believe the bottom line is: These are her own body parts. She is not harming any other animal by consuming these items.
Unless she is producing babies for the sole purpose of having placenta and breast milk, I am pretty sure she will be within the rules of veganism.
Seriously - the milk coming in is very painful and if you are going to help with the drinking of it after the baby is full (mine were never awake OR hungry when the came in and my darling husband would not help) then you need to emulate the way the baby suckles or you will hurt her, too. Watch the baby and learn while it is just colostrum.